Leadership, management and supervision are different activities but unfortunately we have often combined them into the single verb of leadership.  Within a specific role there is aspects of all three of activities and depending upon the action that you are undertaking at the moment it could be more of one activity and less of another. And no role would include only leadership activities 100% of the time each day and every day, it just not happen.  Even a CEO has a lot of time spent in supervisory and management activities in their day.  So don't be caught in the trap that we all need to be seen as leaders all the time  In fact, the best leaders are also good managers and great supervisors.  Anyone who is responsible for the leadership of others must think of themselves as a supervisor first, and to make sure these responsibilities are fulfilled well each day.  Supervision is at the core of the service and duty that you have to those that you lead.

Every person under your supervision is different. They're all different. They're identical in most ways, but not in all ways. You have to study and analyze every individual under your supervision and try to work with them in a way that will be most productive.  John Wooden

Rank does not confer privilege or give power. It imposes responsibility. Peter F. Drucker

A leader leads by example, not by force. Sun Tzu